RPS Thermodynamics of Taub-NUT AdS Black Holes in the Presence of Central Charge and the Weak Gravity Conjecture

TL;DR

This paper explores the thermodynamics of Taub-NUT AdS black holes using a holographic approach, examining phase transitions and verifying the weak gravity conjecture in the context of central charge and critical points.

Contribution

It introduces a novel thermodynamic framework involving central charge and chemical potential, and demonstrates the weak gravity conjecture's validity for Taub-NUT-AdS black holes.

Findings

Identification of supercritical phase equilibrium in $T-S$ processes

Analysis of Hawking-Page phase transition in $$ processes

Verification of the weak gravity conjecture at critical points

Abstract

We study the thermodynamics of the Taub-NUT AdS black holes by Visser holographic method using AdS radius as a constant parameter under the restricted phase space approach. Instead of the variables $P$ and $V$, we deal with the central charge and also chemical potential as a unique couple of conjugate thermodynamic variables. We study some interesting properties of the Taub-NUT black holes e.g. supercritical phase equilibrium in the $T-S$ processes, $Q-\Phi$ and the Hawking-Page phase transition in the $\mu-C$ processes. As a consequence, the consistency of the weak gravity conjecture of multi-charge for Taub-NUT-AdS black holes at critical points is proved. We conclude that in the presence of the central charge and assuming $C=\frac{3}{8}\ell^2$, weak gravity conjecture could be satisfied in the Taub-NUT-AdS black holes with $\hat{n}\ll 1$.